Problem Analysis #probability_24

Motif 3 · Run 1

Python ● execution succeeded

Incorrect

8.57s

2,431 toks

Infron · Motif 3 · 46문항 × 3회 · Python TAR. 131,072 output tokens · 기본 1,800초 · 6+1 turns. ACC는 전체 138회, Pass@1은 각 문항의 첫 유효 시도, Pass@3는 3회 내 정답으로 계산합니다.

Problem Statement

두 사건 A,B에 대하여 $P(A)=\frac25$ , $P(B\mid A)=\frac14$ , $P(A\cup B)=1$ 일 때, $P(B)$ 의 값은?

① $\frac7{10}$ ② $\frac34$ ③ $\frac45$ ④ $\frac{17}{20}$ ⑤ $\frac9{10}$

최종 답은 선택지 번호 1~5 중 하나를 $\boxed{}$ 안에 쓰세요.

Ground Truth

Recorded model response / solution

Reasoning Process

Recorded Python call:

from fractions import Fraction

P_A = Fraction(2, 5)
P_B_given_A = Fraction(1, 4)
P_A_union_B = Fraction(1, 1)

# P(A ∩ B) = P(B|A) * P(A)
P_A_inter_B = P_B_given_A * P_A
print("P(A ∩ B) =", P_A_inter_B)

# P(A ∪ B) = P(A) + P(B) - P(A ∩ B) => P(B) = P(A ∪ B) - P(A) + P(A ∩ B)
P_B = P_A_union_B - P_A + P_A_inter_B
print("P(B) =", P_B)

Tool Output

Execution succeeded P(A ∩ B) = 1/10 P(B) = 7/10

Final Model Output

Answer channel integration error

The provider returned reasoning data, but no scorable content field.

Comparative Analysis (Pprobability_24) (Average across runs)

Averages use reported measurements only. Missing usage is not treated as zero.

Avg Time Taken

Motif 3

42.0

Solar Pro 4

23.1

Grok 4.7

14.6

Union Alpha

14.0

MiMo V2.6 Pro

11.5

Muse Spark 1.3

5.8

DeepSeek V4.1 Flash

4.4

Solar Mini 4 Preview

2.6

Avg Token Usage

Grok 4.7

5,689

Solar Pro 4

4,399

Muse Spark 1.3

3,419

MiMo V2.6 Pro

3,398

DeepSeek V4.1 Flash

2,792

Union Alpha

2,653

Motif 3

2,628

Solar Mini 4 Preview

2,127